The invention described herein may be manufactured and used by or for the Government of the United States of America for governmental purposes without the payment of any royalties thereon or therefor.
The present invention relates to methods and apparatuses for measuring fluid flow, more particularly for measuring vorticity.
Vorticity is a property of fluid flow that may be calculated from the velocity field by the equation
{right arrow over (xcexa9)}=∇xc3x97{right arrow over (u)},xe2x80x83xe2x80x83(1)
where {right arrow over (xcexa9)} is the vorticity vector at a location, and {right arrow over (u)} is the velocity vector at that location. If the flow is assumed to be two-dimensional, equation (1) may be reduced to
xcexa93=dv/dxxe2x88x92du/dy,xe2x80x83xe2x80x83(2)
where xcexa93 is the vorticity component in the z direction, and u and v are the velocity components in the x and y directions, respectively. When velocities are available at discreet locations in space, rather than continuously, equation (2) becomes
xcexa93=xcex94v/xcex94xxe2x88x92xcex94u/xcex94y.xe2x80x83xe2x80x83(3)
Because vorticity is made up of spatial derivatives of velocity, measurement of vorticity requires measurements of velocity at more than one location. Generally, these measurements must be made simultaneously. Among the many applications of hot-wire probes are those involving measurement of vorticity, which requires measurements of velocity at more than one location. Hot-wire probes have been used to simultaneously measure the velocity vector at several locations; however, the hot-wire probes known for measuring vorticity typically require at least six wires, and thus are rather complex.
It is therefore desirable to be capable of measuring vorticity at different locations wherein such measurements need not be made simultaneously.
In view of the foregoing, it is an object of the present invention to provide method and apparatus for measuring vorticity using non-simultaneous velocity measurements at different locations (i.e., velocity measurements which occur non-simultaneously from location to location).
In accordance with many embodiments of the present invention, a method for measuring vorticity relating to the flow of a fluid comprises: sensing the velocity of the fluid at each of at least three locations in the fluid; sensing a reference property of the fluid at each of the three locations; identifying a temporal relationship among the at least three locations in terms of when the sensing of a reference property occurs; and mathematically rendering contemporaneousness of the sensing of the velocity at the at least three locations.
Further according to many embodiments of the present invention, a computer program product comprises a computer useable medium having computer program logic recorded thereon for enabling a computer to determine the vorticity pertaining to the flow of a fluid. The computer program logic comprises: means for enabling the computer to define at least three locations in the fluid; means for enabling the computer to receive information pertaining to the sensing of the velocity of the fluid at each of the at least three locations; means for enabling the computer to receive information pertaining to the sensing of a reference property of the fluid at each of the at least three locations; means for enabling the computer to identify a time relationship among the at least three locations in terms of when the sensing of a reference property occurs; and means for enabling the computer to mathematically render contemporaneousness of the sensing of the velocity at the at least three locations.
Also according to the present invention, a system for determining the vorticity pertaining to the flow of a fluid comprises a machine having a memory. The machine contains a data representation of the vorticity pertaining to the flow of the fluid. The data representation is generated, for availability for containment by said machine, by the method comprising: defining at least three locations in the fluid; receiving information pertaining to the sensing of the velocity of the fluid at each of the at least three locations; receiving information pertaining to the sensing of a reference property of the fluid at each of the at least three locations; identifying a time relationship among the at least three locations in terms of when the sensing of a reference property occurs; and mathematically rendering contemporaneousness of the sensing of the velocity at the at least three locations.
The present invention provides a methodology for measuring vorticity using velocity measurements taken at least two different locations. This invention is particularly efficacious when measuring vorticity using velocity measurements which are effectuated non-simultaneously at least two different locations. Conventionally, vorticity of a fluid is determinable only if all of the velocity measurements are effectuated simultaneously. Thus, a primary advantage of this invention is that it allows vorticity to be measured using non-simultaneous velocity data. This is a significant advantage because it allows simpler and/or less costly measurement systems than are required for simultaneous measurements of velocity.
The above-noted concurrently filed application entitled xe2x80x9cX-Wire Probe for Velocity Measurements Near the Downstream Edge of an Aperturexe2x80x9d discloses an inventive x-wire probe device for effecting velocity measurements. The x-wire probe according to that invention lends itself to efficacious use in association with the fluid vorticity measurement methodology according to this invention. An advantage of using the inventive x-wire probe disclosed in the concurrently filed application derives from the relative simplicity of such inventive x-wire probe as compared with the more complex hot-wire probes which have been known for measuring vorticity. Nevertheless, it is emphasized that the inventive vorticity measurement method disclosed herein admits of application under a variety of fluidic contexts and circumstances as well as through implementation of a variety of probe types.
Other objects, advantages and features of this invention will become apparent from the following detailed description of the invention when considered in conjunction with the accompanying drawings.
Hereby incorporated herein by reference is the following 180-page U.S. Navy technical report which discloses various aspects of the present invention: Paul J. Zoccola, Jr., xe2x80x9cExperimental Investigation of Flow-Induced Cavity Resonance,xe2x80x9d NSWCCD-TR-2000/010, June 2000, Signatures Directorate Technical Report, Naval Surface Warfare Center, Carderock Division, West Bethesda, Md., 20817-5700. The substance of this report is also available under reference number 9969545 from Bell and Howell Company, Skokie, Ill. in the form of the inventor""s doctoral dissertation. This dissertation is also expected to be available from the library of the Catholic University of America, Washington, D.C.